Nonadiabatic Electron Transfer: Exact Analytical Expression of through-Conjugated-Bridge Effective Coupling and Its Asymptotics and Zeros

Important issues facing model-based approaches to tunneling transport in molecular junctions

Extensive studies on thin films indicated a generic cubic current-voltage I-V dependence as a salient feature of charge transport by tunneling. A quick glance at I-V data for molecular junctions suggests a qualitatively similar behavior. This would render model-based studies almost irrelevant, since, whatever the model, its parameters can always be adjusted to fit symmetric (asymmetric) I-V curves characterized by two (three) expansion coefficients. Here, we systematically examine popular models based on tunneling barriers or tight-binding pictures and demonstrate that, for a quantitative description at biases of interest (V slightly higher than the transition voltage Vt), cubic expansions do not suffice. A detailed collection of analytical formulae as well as their conditions of applicability is presented to facilitate experimentalist colleagues to process and interpret their experimental data obtained by measuring currents in molecular junctions. We discuss in detail the limits of applicability of the various models and emphasize that uncritically adjusting the model parameters to experiment may be unjustified because the values deduced in this way may fall in ranges rendering a specific model invalid or incompatible to ab initio estimates. We exemplify with the benchmark case of oligophenylene-based junctions, for which the results of ab initio quantum chemical calculations are also reported. As a specific issue, we address the impact of the spatial potential profile and show that it is not notable up to biases V ≳ Vt, unlike at higher biases, where it may be responsible for negative differential resistance effects.

Electron transfer in proteins: nonorthogonal projections onto donor-acceptor subspace of the Hilbert space

We develop nonorthogonal projectors, called Löwdin projectors, to construct an effective donor-acceptor system composed of localized donor (D) and acceptor (A) states of a long-distance electron transfer problem. When these states have a nonvanishing overlap with the bridge states these projectors are non-Hermitian and there are various possible effective two-level systems that can be built. We show how these can be constructed directly from the Schrödinger or Dyson equation projected onto the D-A subspace of the Hilbert space and explore these equations to determine the connection between Hamiltonian and Green function partitioning. We illustrate the use of these effective two-level systems in estimating the electron transfer rate in the context of a simple electron transfer model.

Electron transmission through molecules and molecular interfaces

Electron transmission through molecules and molecular interfaces has been a subject of intensive research due to recent interest in electron-transfer phenomena underlying the operation of the scanning-tunneling microscope on one hand, and in the transmission properties of molecular bridges between conducting leads on the other. In these processes, the traditional molecular view of electron transfer between donor and acceptor species gives rise to a novel view of the molecule as a current-carrying conductor, and observables such as electron-transfer rates and yields are replaced by the conductivities, or more generally by current-voltage relationships, in molecular junctions. Such investigations of electrical junctions, in which single molecules or small molecular assemblies operate as conductors, constitute a major part of the active field of molecular electronics. In this article I review the current knowledge and understanding of this field, with particular emphasis on theoretical issues. Different approaches to computing the conduction properties of molecules and molecular assemblies are reviewed, and the relationships between them are discussed. Following a detailed discussion of static-junctions models, a review of our current understanding of the role played by inelastic processes, dephasing and thermal-relaxation effects is provided. The most important molecular environment for electron transfer and transmission is water, and our current theoretical understanding of electron transmission through water layers is reviewed. Finally, a brief discussion of overbarrier transmission, exemplified by photoemission through adsorbed molecular layers or low-energy electron transmission through such layers, is provided. Similarities and differences between the different systems studied are discussed.